Path selection device, program and method

ABSTRACT

A start node acquires coupled state information indicating a connectibility of nodes from a network. By executing simulation in accordance with a computational model constructed based on the coupled state information, the start node determines for each node a first link that transmitted an oscillation or a signal first to the node. A path that extends from a target node to the start node via the first link of intermediate nodes is selected.

TECHNICAL FIELD

This invention relates to a path selection method for a networkincluding a plurality of nodes and a plurality of links, such as aninformation network or a traffic network, and more particularly, tosimulation of required time for each path in a modeled network, and therequired time.

BACKGROUND ART

There has conventionally been considered a path selection problem in anetwork as a search for a shortest path connecting two points.Representative types of the network include a traffic network regardingtraffic of cars and the like, and an information network regardinginformation communication.

The most famous method for shortest path search is the Dijkstra method.The Dijkstra method is an algorithm that is substantially optimum interms of a computational theory, but in a case of application to a realproblem, has a problem in that, when a shortest path connecting distantpoints is to be determined, the problem cannot be solved in realistictime because many parts of map information (map data) need to beaccessed, for example. An image of the algorithm of the Dijkstra methodis to gradually determine a shortest path from a start node (startingpoint) to a neighboring node, and when arriving at a target node(destination) and there is no probability that another path is theshortest path, end the computation.

In order to solve this problem, some approaches have been taken.

As a most simple method of decreasing the computation time, there is amethod of performing the Dijkstra method from both a start point and anend point to narrow down a search range. There is also a method calledthe A* algorithm for preferentially searching a direction with a smallerstraight-line distance to the destination. Those methods are reduced incomputation time as compared to the Dijkstra method, but still have aproblem in that an enormous amount of time is needed for large-scaledata.

Another method is a heuristic method of assuming that when movingbetween distant areas, a kind of predetermined route is taken, tothereby omit the intermediate search. As a subspecies, there is also amethod of forming roads into a hierarchy of a network including roadsused for traveling a long distance, such as expressways and highways,and a network including the other roads, and after first determining theshortest path from each of the current position and the destination tothe nearest highway, solving the shortest path problem on the highway.Those can be considered as approaches that give up on optimization.

In recent years, there have been adopted approaches in which, forexample, a certain kind of preprocessing is performed on the mapinformation (map data) so as to find a solution in a short time when theshortest path is determined later. The most famous of those approachesare the bit vector method and the highway hierarchy method.

In the bit vector method, the map is divided into several areas, and fora set of each node and an area, from among links connecting to the node,a used link for use by the shortest path from the vertex to the node inthe area is selected in advance. In searching for the shortest path, thesearching is omitted by searching only the used link in a direction froma desired node to an area including the destination. The problems arethat the preprocessing takes time and that an increase in memory iscaused by storing the used link and the like.

In the highway hierarchy method, links for long distance are determinedin advance so that a link for long distance is reached in k links from astart node, and after getting off the link for long distance, the targetnode is reached in k links. In other words, the link for long distancesatisfying the above-mentioned conditions are determined in advance inthe approach. The approach is advantageous in that the preprocessingends when the shortest path is determined only for nodes that are within2k+1 links from each node, and hence the preprocessing time is shorterthan the other approaches. The problem is that there is no guaranteethat the network contains the link for long distance.

The technologies of shortest path search have been outlined above, andhave been working with some success in a network in which nodes andlinks are stable to some extent as in the traffic network. However, inthe case of the information network in which the relationship betweennodes and links changes dynamically, it is difficult to adapt theabove-mentioned algorithms in a simple manner. For example, in the caseof the information network, the preprocessing and the like cannot beperformed realistically. This is because the preprocessing requires asomewhat stable network (that changes little with time) as aprecondition.

As a shortest path search for the information network, the followingapproach has been conventionally used.

The shortest path search generally used in a large scale informationnetwork is a path control protocol called Open Shortest Path First(OSPF). This protocol uses the Dijkstra algorithm. This OSPF has afeature in that, while the routers exchange copies of the entire pathtables of their own in the conventional distance-vector path controlprotocol, the routers exchange only the link states and each routercomputes the shortest path. Therefore, the OSPF has an advantage thatthe amount of data to be exchanged between the routers is significantlysmall as compared to the conventional distance-vector algorithm andhence the amount of data exchange can be made smaller irrespective ofthe scale of the network system.

In actual operation, the OSPF performs the path selection by dividing anautonomous system (AS), which is a set of operating routers, into aplurality of areas so that all routers belonging to one area areconfigured to have the same link state database and each of the routerscomputes the shortest path from the router to all the destination basedon the link state database.

However, the OSPF performs the shortest path computation with the littlecomputational resource of the router, and hence has had problems in thatthe restriction in computational resource limits the area and does notallow the shortest path computation to be performed frequently. In thecase of the information network, the network status changes dynamicallyas compared to the traffic network, and hence while the shortest pathcomputation essentially needs to be performed in real time if possible,such ideal situation is hard to achieve.

In addition, irrespective of whether the relationship between the nodesand the links is stable in time, the shortest path computations arecommon in determining the shortest path by computing and comparing thelengths of the paths.

Literatures describing the technologies relating to this inventioninclude Japanese Patent Application Laid-open Nos. 2009-141425 and2010-041429 (hereinafter referred to as Patent Literatures 1 and 2,respectively). The technologies disclosed in those patent literaturesare both technologies involving transmitting a search packet to the realnetwork and selecting the path based on the state of the packet.According to such methods, in order to grasp the network state of theentire path, there is a need to actually transmit to the network thenumber of packets corresponding to the scale of the network and thenobserve the state. Therefore, it is considered that applying suchtechnologies to a large-scale network to select a path is difficult.

DISCLOSURE OF THE INVENTION Problem to be Solved by the Invention

As described above, the conventional shortest path search algorithmshave the problem in that the computation takes time or the enormouscomputational resources are consumed. Therefore, especially in equipmentsuch as the router in which the computational resources are limited, ithas been impossible to search for the shortest path and select the pathin real time. This is an important problem especially in an informationnetwork in which the network state changes dynamically, and causes aproblem in that a network response that is satisfactory to the usercannot be provided due to the information transmission delay.

In recent years, the information network is continuously expanding. Thismeans that the shortest path search becomes more difficult, which leadsto the expectation that the users' convenience is compromised year afteryear. This invention has been devised in view of the above-mentionedsituation, and provides a technology for significantly reducing thecomputational time and the computational resources of the conventionalshortest path search.

Solution to Problem

In order to solve the above-mentioned problem, according to an aspect ofthis invention, there is provided a path selection device, including:network information acquisition means for acquiring, by a start nodewhich is a source of an oscillation or a signal to be simulatedregarding a transmission process in a network and is one node in thenetwork, coupled state information of the network indicating aconnectibility of nodes in the network from the network; network stateanalysis means for determining, by an arithmetic unit of the start nodeexecuting the simulation in accordance with a computational modelconstructed based on the coupled state information, when n (n is anatural number) links connected to the one node in the network arecalled a first link, a second link, . . . , an n-th link in order from alink that has transmitted the oscillation or the signal first to the onenode, at least the first link for each of the nodes in the network; andnetwork path selection means for selecting by the start node a path thatextends from a target node, which is one node in the network other thanthe start node, to the start node via the first link of intermediatenodes as a desired path between the start node and the target node.

Further, according to another aspect of this invention, there isprovided a program for causing a computer to function as: networkinformation acquisition means for acquiring, by a start node which is asource of an oscillation or a signal to be simulated regarding atransmission process in a network and is one node in the network,coupled state information of the network indicating a connectibility ofnodes in the network from the network; network state analysis means fordetermining, by an arithmetic unit of the start node executing thesimulation in accordance with a computational model constructed based onthe coupled state information, when n (n is a natural number) linksconnected to the one node in the network are called a first link, asecond link, . . . , an n-th link in order from a link that hastransmitted the oscillation or the signal first to the one node, atleast the first link for each of the nodes in the network; and networkpath selection means for selecting by the start node a path that extendsfrom a target node, which is one node in the network other than thestart node, to the start node via the first link of intermediate nodesas a desired path between the start node and the target node.

Further, according to still another aspect of this invention, there isprovided a path selection method, including the steps of: acquiring, bya start node which is a source of an oscillation or a signal to besimulated regarding a transmission process in a network and is one nodein the network, coupled state information of the network indicating aconnectibility of nodes in the network from the network; determining, byan arithmetic unit of the start node executing the simulation inaccordance with a computational model constructed based on the coupledstate information, when n (n is a natural number) links connected to theone node in the network are called a first link, a second link, . . . ,an n-th link in order from a link that has transmitted the oscillationor the signal first to the one node, at least the first link for each ofthe nodes in the network; and selecting, by the start node, a path thatextends from a target node, which is one node in the network other thanthe start node, to the start node via the first link of intermediatenodes as a desired path between the start node and the target node.

Effect of the Invention

According to this invention, it is possible to provide the pathselection method and device which require fewer resources and performcomputation at high speed. This also allows a path selection to beperformed in a network with high flexibility (enormous number of nodesand links). In addition, the path selection method may be executed athigh frequency, and hence an appropriate path selection may be executedeven in a network in which the situation changes dynamically.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a diagram illustrating a path selection method according to anembodiment of this invention, and illustrates a network in which aplurality of nodes, which are likened to oscillators, are connected inseries.

FIG. 2 is a graph showing, in a network including five nodes, Node 1,Node 2, . . . , Node 5, which are connected in series, a process inwhich phases of oscillation that has occurred in Node 1 are transmittedto other nodes.

FIG. 3 illustrates an example of a network overview on the left side ofthe arrow, and a tree structure obtained based on the network overviewand the first link of each node on the right side of the arrow.

FIG. 4 includes graphs showing methods of detecting that a phase hastransmitted to a node, of which (a) is a graph showing the method ofdetecting based on an amplitude of the node, and (b) is a graph showingthe method of detecting based on a period of the node.

FIG. 5 is a modification of the path selection method of the firstembodiment, and is a diagram illustrating the path selection method inwhich virtual oscillators for phase detection for identifying a nodethat has transmitted the oscillation to a link are provided.

FIG. 6 is a diagram illustrating detection of an oscillation shift in anoutward path and an inward path of a link by an oscillator for phasedetection provided in the network including five nodes.

FIG. 7 is a graph showing oscillations of Node 1, Node 2, . . . , Node 5of FIG. 6.

FIG. 8 is a graph showing oscillations of the oscillators for phasedetection for the outward path of Link 1, Link 2, . . . , Link 5 of FIG.6.

FIG. 9 is a graph showing oscillations of the oscillator for phasedetection for the inward path of Link 1, Link 2, . . . , Link 5 of FIG.6.

FIG. 10 is a block diagram illustrating a path selection device ofExamples 1 and 2.

FIG. 11 is a diagram illustrating a network for which a shortest pathsearch has been performed by using the path selection device of Examples1 and 2.

FIG. 12 is a graph showing a relationship of computation time and thenumber of nodes of the shortest path searches performed for the networkof FIG. 11 with the conventional path selection device using theDijkstra method and the path selection device of Example 1.

FIG. 13 is a graph illustrating a relationship between computation timeand the number of nodes of the shortest path searches performed for thenetwork of FIG. 11 with the conventional path selection device using theDijkstra method and the path selection device of Example 2.

FIG. 14 is a diagram illustrating, when a failure occurs in a node on analready-determined shortest path in a period in which information istransmitted from a start node and the information arrives at a targetnode, how a node that has acquired failure node information determines anew shortest path so that a network of this invention autonomouslyavoids the failure.

BEST MODE FOR EMBODYING THE INVENTION

In a path selection method of this invention, lengths of paths in anetwork are not compared to determine the shortest path, and the lengthsof the paths do not need to be directly computed. According to the pathselection method of this invention, a start node in the network islikened to an oscillator or a signal source, and a process in which anoscillation/signal is transmitted from the start node to other nodes issimulated on a computer, to thereby determine a link through which theoscillation/signal is transmitted first to the node.

In a network system of this invention, each node in the network performsa path selection. Moreover, prior to the path selection, each nodefunctions on a precondition that information on an overall image of thenetwork has been acquired correctly to some extent from the network.This precondition is the same as that in the OSPF described above. Theoverall image information of the network specifically includes topology(structure) information of the network and coupled state information ofthe network. Those pieces of information are hereinafter also simplyreferred to as overall image information, topology information, andcoupled state information, respectively. The “coupled state informationof the network” refers to information indicating a coupled state of thenetwork or a connectibility of the nodes, and includes, for example, adistance of a link between certain nodes, an upper limit (capacity) ofan information flow through the link between the certain nodes, and aspeed of the information flow through the link between the certainnodes. In this embodiment, as the coupled state information, the use ofthe distance between the nodes is mainly described, but a person skilledin the art could easily understand that general physical quantitiesregarding the coupled state of the network can be used. Moreover, thedescription is given herein assuming an information network, but thesame applies to other networks such as a traffic network.

The phrase “to some extent” is used herein because as the networkbecomes larger, it becomes more difficult to share latest informationbetween distant nodes, which makes it difficult to know the overallimage of the network correctly at a certain time. In addition, when thelink status (connectibility) changes every minute as in the informationnetwork, it is also difficult to know the overall image of the networkcorrectly. According to this invention, an effective path search can beperformed even when the overall image information of the network is notalways perfect. The reason is described later.

First Embodiment

The path selection method according to a first embodiment of thisinvention is described based on a network system 1. This is the mostbasic form of the invention of the subject application. The networksystem 1 is a network in which N (N is a natural number) nodes: Node 1,Node 2, . . . , Node N are connected in the stated order in series. Eachof Node 1, Node 2, . . . , Node N is equipment including an arithmeticprocessing unit, and more specifically, equipment such as an accessserver of an internet access provider or a router. Each of the nodes ofthe network executes the following path selection method.

As described above, the nodes know the overall image of the networkcorrectly to some extent, and based on the overall image, constructs acomputational model as illustrated in FIG. 1 to perform a pathcomputation. In this embodiment, the distance between the nodes is usedas the coupled state information, which is an example of a pathcomputation of a shortest path. When the coupled state information is areciprocal of flowability of the information flow or the like, the pathcomputation of the fastest information transmission path is performed.For simple description, FIG. 1 is a diagram in which the invention ofthe subject application is applied to a network in which a plurality ofnodes are arrayed in line. Each of the nodes is connected to an adjacentnode via only one link. Nonlinear oscillators are provided to a positioncorresponding to the nodes.

In this embodiment, a Van der Pol oscillator is assumed as the nonlinearoscillator, and the distance of the link connecting the nodes isreplaced by a diffusion coefficient D of the oscillation. The oscillatoris not limited to the Van der Pol oscillator, and various oscillatorsmay be used instead. The coupled state information has a predeterminedrelationship with the diffusion coefficient D, and in this embodiment,the distance (length) of the link needs to be converted to the diffusioncoefficient D with some function. In this embodiment, on the analogy ofthermodynamics, the diffusion of the oscillation of the oscillator isexpressed by a diffusion equation. The equation expressing the diffusionof the oscillation of the oscillator may be another equation as long asthe diffusion of the oscillation may be described. As a result, thenetwork of the nonlinear oscillators of FIG. 1 may be described by thefollowing equation.

$\begin{matrix}\left. \begin{matrix}{\frac{\partial{x\left( {r,t} \right)}}{\partial t} = {{ɛ\left( {x - \frac{x^{3}}{3}} \right)} - y + {D_{ij}\frac{\partial^{2}x}{\partial r^{2}}}}} \\{\frac{\partial{y\left( {r,t} \right)}}{\partial t} = {{\alpha^{2}(r)}x}}\end{matrix} \right\} & \left( {{Math}.\mspace{14mu} 1} \right)\end{matrix}$

In the equation, D with the index ij represents the diffusioncoefficient between the i-th node and the j-th node. The term with Dijrepresents a relationship between Oscillator i and Oscillator j. ε and αare parameters determining the characteristics of the oscillation. Inthe above equation, x represents an amplitude of the oscillator, y is aterm physically representing an effect of a spring and represents thespring, and r represents a position of the oscillator. t representstime. Following such equation that is capable of describing thediffusion of the oscillation as Equation 1, motions of all theoscillators are simulated by considering that Oscillator 1, Oscillator2, . . . , Oscillator N respectively corresponding to Node 1, Node 2, .. . , Node N of the network move. When an initial value of theoscillator corresponding to the node at a starting point is changed, theoscillation is started. Motions of the oscillators corresponding to thenodes other than the starting point are also subject to the aboveequation, and hence the oscillation of the oscillator of the node at thestarting point is transmitted sequentially to the other oscillatorsdepending on a transmission state of the oscillation represented by theterm of Dij. At this time, the link that transmits the oscillation firstto the node is determined for each of the nodes, and based on thosedetermination results, the shortest path from the start node to each ofthe nodes is determined.

After setting the computational model as described above and thensetting an external force or the initial value of the nonlinearoscillator of the start node (the node corresponding to the own nodethat performs the computation), the nonlinear oscillator starts theoscillation. When ε and α are appropriately set in advance, theoscillation converges to a fixed oscillation called a limit cycleirrespective of the external force and the initial value.

The oscillation that has occurred in the start node is transmitted tothe surrounding nodes via the links having the diffusion coefficient D,and the nonlinear oscillators surrounding the start node eventuallystart the oscillation. The time at which the surrounding nonlinearoscillators start the oscillation is equal to the time at which a phaseof the oscillation of the start node arrives, and hence the nodes closerto the start node start the oscillation earlier.

FIG. 2 shows how phases of the oscillation that has occurred in Node 1are transmitted among the five nodes: Node 1, Node 2, . . . , Node 5connected in series. At time 0, Nodes 2 to 5 do not oscillate. It can beseen that the oscillation of Node 1 as the start node is sequentiallytransmitted to Node 2, Node 3, . . . .

FIG. 2 shows the example in which the nodes other than the start node donot oscillate at first, but in a case of the nonlinear oscillator, aphenomenon called entrainment in which the oscillation having highfrequency converges to the oscillation having low frequency exists.Therefore, when the start node is caused to oscillate at the highestfrequency and the other nodes are caused to oscillate at frequencieslower than that of the start node, and when the phase of the start nodearrives, frequencies of the other nodes sequentially converge to thehigh frequency of the start node. This transmission of the frequency canbe used in detecting the phase transmission. In a linear oscillator,this convenient entrainment phenomenon does not occur and hence thenumber of variations in detecting the phase transmission is reduced, buta linear oscillator may be used without any problem for simpletransmission of the oscillation (case as shown in FIG. 2).

For simple description, a one-dimensional linear network has been usedfor description with reference to FIG. 1, which makes it difficult toimagine whether the network path selection can be performed with theabove-mentioned phenomenon, but when the above-mentioned phenomenon isutilized, the network path selection can be performed.

Even when a plurality of links are connected to one node, the phase istransmitted via a path through which the phase is transmitted first,that is, the shortest path. Therefore, when focusing on a node, it canbe considered that the link that has transmitted the phase to the nodefirst forms the shortest path to the node. When m (m is a naturalnumber) links are connected to a node, the links that have transmittedthe phase to the node first, second, . . . , m-th are hereinafter calledthe first link, the second link, . . . an m-th link, respectively in thestated order. When the phase is transmitted via a link connected to thenode and the first link is determined, the second and subsequent linksof the node are disqualified for forming the shortest path. Therefore,when only the shortest path search is performed, only the first link maybe recorded and the other links may be ignored.

In order to determine the shortest path from the start node to the node,a path that sequentially passes through the first links of theintermediate nodes from the first link of the node to return to thestart node is determined. Similarly, a path that returns to the startnode from each of the nodes other than the start node in the network isdetermined. In this way, with the start node as a vertex, the shortestpaths to the other nodes are expressed in a tree form. This can be usedto determine to which link the own node is to transmit information inorder to transmit the information a desired target node.

The network overview on the left side of FIG. 3 illustrates an examplein which the first links of the nodes are indicated by thick lines andthe second and subsequent links are indicated by thin lines. When onlythe first links are extracted from the network overview, a treestructure on the right side of FIG. 3 can be obtained. For example, theshortest path from Node N1 as the starting point or the start node ofthe network overview on the left side of the figure to Node N7 can beseen from a tree structure on the right side of the figure as Nodes N1,N2, N5, N6, and N7.

When not only the shortest path but also the links to the second andthird nodes are to be found, not only the link that has transmitted thephase to a node first but also a time at which the phase is transmittedis recorded for each link so that the transmission times of the linksare compared to determine the places of the links.

Several methods are contemplated to detect that the phase has beentransmitted to the node, and two typical methods are shown together inFIGS. 4.

The first method is to detect an amplitude change in the simulation ofthe oscillator corresponding to the node. When the phase is transmittedfrom an oscillator, oscillators that have not oscillated startsoscillation. The method uses this fact and when a certain amplitude isdetected in the oscillator corresponding to the node, it is determinedthat the phase has been transmitted to the oscillator, that is, thenode. As shown in FIG. 4( a), a slice level for detecting phasetransmission is set, and a motion of the oscillator corresponding to thenode is simulated, for example, in accordance with an equation such asEquation 1. At a time when the amplitude of the simulated oscillator hasexceeded the slice level for detecting phase transmission, it isdetermined that the phase has been transmitted to the node.

The second method is to detect a period of the oscillation. Oscillatorsto which the oscillation has been transmitted from an oscillator thatoscillates at a frequency come to oscillate with the same period as thatof the oscillator as the transmission source. This fact is used tomonitor the period of the oscillator simulated in accordance with theequation such as Equation 1, and when the same slice level for theperiod corresponding to the period of the oscillator of the start nodehas been reached, it is determined that the phase has been transmittedfrom the oscillator of the start node to the oscillator of the node.

The methods of detecting the phase have been described above, but whensome links are coupled to one node, there may be a time when it is alittle troublesome to determine from which link the phase has arrived.This is because, when the difference in phase transmission from thelinks is slight and the phase is actually transmitted from a pluralityof links before being detected by the above-mentioned methods, in orderto confirm from which node the phase has been transmitted first, analgorithm for analyzing the state of the oscillation in the link, thestate of the oscillation of the previous node, and the like needs to beused.

Therefore, the inventors of the subject application have also devised animproved path selection method as illustrated in FIG. 5. For simpledescription, as with FIG. 1, a one-dimensional linear network is usedfor description. FIG. 5 is different from FIG. 1 in that oscillators forphase detection for detecting from which node the phase has beentransmitted are virtually provided to each link. As described above, theoscillators corresponding to the nodes are simulated as moving inaccordance with an equation capable of describing the diffusion of theoscillation, such as Equation 1, and motions of the oscillators forphase detection are also simulated in accordance with the same equation.The same applies to the diffusion coefficient D.

For convenience, the two oscillators are called an outward path and aninward path, respectively. In this embodiment, each of those oscillatorsfor phase detection is also formed by the Van der Pol oscillator. Twooscillators for phase detection are provided to each link for theoutward path and the inward path, and each oscillator transmits only theoscillation of the node located on the opposite side of the oscillator,and at a time when the oscillation is transmitted to the oscillatoritself, determines that the oscillation has been transmitted from thenode located on the opposite side of the oscillator. In this manner, thetransmissions of the oscillation on the outward path side and the inwardpath side are clearly distinguished, and it can be determined from whichside the phase has been transmitted first.

Referring to FIG. 5, two nodes are provided adjacent to each other inthe network, and Oscillator 1 and Oscillator 2 are provided asoscillators corresponding to the nodes. Oscillator 1 and Oscillator 2are connected via a link. Near an end portion on the Oscillator 1 sideof the link, an oscillator for phase detection (inward path) isvirtually provided as a virtual oscillator that does not correspond tothe nodes in the network. In the same manner, an oscillator for phasedetection (outward path) is virtually provided near an end portion onthe Oscillator 2 side of the link. The oscillator for phase detection(inward path) is caused to transmit only the oscillation from Oscillator2 and not to transmit the oscillation from Oscillator 1. In the samemanner, the oscillator for phase detection (outward path) is caused totransmit only the oscillation from Oscillator 1 and not to transmit theoscillation from Oscillator 2.

Now, a network in which five nodes: Node 1, Node 2, . . . , Node 5 areconnected as illustrated in FIG. 6 is considered. The numerals incircles in the figure are link numbers indicating the correspondinglinks, and for example, the link between Node 1 and Node 2 has a linknumber of 1. FIG. 6 illustrate Link 1, Link 2, . . . , Link 5. The valueof D written on the side of each of the link numbers is a valueindicating the connectibility of the nodes in the link, and correspondsto the diffusion coefficient D in Equation 1 above. Each of Links 1, 2,. . . , 5 is provided with the oscillators for phase detection (notshown) for the outward path and the inward path. At this time, resultsobtained by simulating oscillations of the oscillators corresponding toNode 1 to 5, the oscillators for phase detection (outward path) in Links1 to 5, and the oscillators for phase detection (inward path) in Links 1to 5 are shown in FIGS. 7 to 9. In particular, it can be seen from thecomparison of FIGS. 8 and 9 that the oscillations of the outward pathand the inward path are slightly shifted, which allows to determinewhich path is the shortest path clearly.

This embodiment allows easy parallelization of the computation, andhence is compatible with hardware that is good at parallel computation,such as GPGPU. Further, in contrast to a second embodiment describedbelow, the distance between the nodes may be treated as a continuousvalue.

Second Embodiment

Next, a path selection method according to the second embodiment of thisinvention is described. In the first embodiment, the nodes are likenedto oscillators and the links are likened to transmission media of theoscillation so that the motions of the nodes when the physical phasesare transmitted between the nodes are simulated on the computer. Incontrast, in this embodiment, there is constructed such computationalmodel that every link in the network is divided to the number ofsections, the number being determined depending on the physicalquantities (for example, distance, transmission speed, and the like ofthe link) regarding the link, and one of the divided section and a unitof time are correlated to simulate a propagation state of a signal inthe network, that is, the process in which the signal transmitted by thestart node is propagated to the other nodes. A unit of quantity of thephysical quantities indicating the coupled state of the network (orlink) is set in association with the unit of time, and then the physicalquantities of the link are changed discretely every unit of time toconstruct such a model as to simulate the propagation state of thesignal in the link. For example, when the distance of the link is usedas the physical quantity indicating the coupled state of the network,the point to which the signal is transmitted between one end to theother end of the link, which is expressed by the moving distance of thesignal in the unit of time, that is, an integer multiple of a unit ofdistance, is the transmission state of the signal in the link. A casewhere the distance of the link is used as the physical quantity of thelink is considered here. The signal transmitted from the start nodemoves in the link, and the movement of the signal in the link untilreaching each of the other nodes is virtually simulated. It is assumedthat the signal is transmitted in the link at a constant speed, and thatwhen the signal is input from a link to the node, the signal is branchedto be output from all the links including the link at the time of theinput. Moreover, it is assumed here that all the links in the networkhave a uniform transmission speed.

As in the first embodiment, prior to the path selection, each of thenodes acquires the overall image information of the network, that is,the topology information and the coupled state information of thenetwork from the network. The distance between the nodes, that is, thedistance of the link is described here to be acquired as the coupledstate information.

The distance by which the signal is transmitted in the link in the unitof time is called the unit of distance. The unit of distance is at mosta distance of the shortest link in the network, and is set depending onthe required accuracy. When a smaller unit of distance is used, thecomputation accuracy becomes higher but the computational load becomeslarger. When all distance ratios between the links in the network can beexpressed by integers, the greatest common divisor of the integers maybe used as the unit of distance to achieve both the high computationaccuracy and low computational load.

Obviously, it takes 2 units of time for the signal to pass through thelink having 2 units of distance, and 3 units of time to pass through 3units of distance. In this manner, when all the links in the network areapproximated by integer multiples of the unit of distance, the signalpasses through any link in the network in an integer multiple of theunit of time, and the units of time that have elapsed since the signalhas entered the link directly indicates the current position of thesignal in the link.

Therefore, a counter which is activated and starts counting immediatelywhen the signal enters the node at one end of the link, increments thecount by one every time the unit of time is elapsed, and counts up tothe value equal to an integer value approximating the distance of thecorresponding link by an integer multiple of the unit of distance isprovided so as to correspond to each link in the network. In suchcounter, the value of the counter reaching the upper limit means thatthe signal that has entered from the node at one end of thecorresponding link arrives at the node at the other end of the link.Such counter is provided for each node in the network, and the values ofall the counters that are currently active in the network areincremented by 1 every unit of time, to thereby simulate the process inwhich the signal transmitted from the start node is transmitted to theother nodes in the network.

In order to obtain a reasonable result in the first embodiment, oneperiod is divided into units of time on the order of about severalthousands, and each time the unit of time has elapsed, arithmeticprocessing of solving the equation such as Equation 1 for the time isgenerated. When the process in which the oscillation is transmitted fromone end to the other end of a link is simulated, if the oscillationlasts for 100 periods, during which about several hundred thousand unitsof time elapse, and hence the above-mentioned arithmetic processing isexecuted about several hundred thousand times. Further, the arithmeticprocessing is arithmetic processing including scientific computing suchas differential computation, and is a floating-point operation.Therefore, when the entire computational loads necessary for thesimulation are compared, the first embodiment is not so advantageous ascompared to approaches based on the Dijkstra method. However, theapproach of the first embodiment allows easy parallelization, and hencewhen the parallel computation is performed, the processing may beexecuted in a shorter time than the approaches based on the Dijkstramethod. Note that, in general, the approaches based on the Dijkstramethod are difficult to parallelize.

As compared to the first embodiment described above, in the secondembodiment, the unit of time may be elongated to reduce the requiredcomputational load. For example, in this embodiment, though depending onthe required computation accuracy and the variation between thedistances of the links in the network, the distance of the shortest linkin the network may be set as the unit of distance, and in this case, oneunit of time elapses in the simulation of signal passage through theshortest link. Further, the processing to be executed each time the unitof time elapses in the second embodiment is essentially processing ofdetermining whether the counter is active for each link and adding 1 tothe value of the active counters. This processing imposes less load ascompared to the arithmetic processing of the scientific computing suchas the differential computation. In other words, in the secondembodiment, the number of arithmetic processing to be executed is small,and the load of the arithmetic processing to be executed each time islight.

In the first embodiment, in order to identify the link that hastransmitted the oscillation to the node, the oscillators for phasedetection as in FIG. 5 are provided. In order to identify thetransmission direction of the signal, in this embodiment, two counters,that is, a counter for the outward path and a counter for the inwardpath may be provided for each link. In general, the nodes are connectedto both ends of one link, respectively. The counter for the outward pathsets one node as an associated node, and the counter for the inward pathsets the other node as an associated node. When the associated node ofthe counter for the outward path detects the transmission of the signal,the counter for the outward path starts counting in response thereto.The counter for the inward path starts counting in the same manner.

Next, the simulation processing performed in this embodiment isdescribed. In this processing, the process in which the signaltransmitted from the start node moves through the link in the network issimulated.

At the same time the start node transmits the signal, a counter havingthe start node as the associated node is activated. When a plurality oflinks are connected to the start node, all the plurality of counterscorresponding to the links are activated. The time at which the signalis transmitted from the start node is hereinafter denoted as t=0, andtimes after 1, 2, . . . , n units of time have elapsed are denoted ast=1, 2, . . . n, respectively.

Each time one unit of time is elapsed, the values of all the activecounters are incremented by 1. At t=1, the values of all the countershaving the start node as the associated node are 1, which indicates thatthe signal is traveling the position away from the start node by oneunit of distance in the links connected to the start node.

When one of the links connected to the start node has 2 units ofdistance, the counter of the link finishes counting at t=2. The factthat the counter has finished counting means that the signal transmittedor input from one of the two nodes connected to the link has arrived atthe other node. At the same time the signal arrives at the node, thelink, the node, and the time are recorded in association with oneanother, and a counter having the node as the associated node isactivated. As with the activation of the counter at the start node, whenthere are a plurality of counters having the node as the associatednode, all the counters are activated.

Thereafter, every time one unit of time is elapsed, the counter that hasbeen activated as described above is caused to count up by 1 along withthe already-active counters. When any one of the active countersfinishes counting and the signal arrives at the node, an operation ofactivating all counters having the node as the associated node isrepeated. When there is no counter having as the associated node thenode at which the signal arrives when the counting is finished, no newcounter is activated.

As a result of the simulation described above, for each of the nodes inthe network, the node, the link which has transmitted the signal to thenode, and the arrival time are recorded in association with one another.When only the shortest path is to be determined, the second embodimentis similar to the first embodiment in that only the first link of eachnode needs to be recorded, and in this case, based on the known networktopology and the first link of each link, a tree structure similar tothat of FIG. 3 may be generated.

In this embodiment, the computation step (time) and the distance of thelink are correlated as the unit of time and the unit of distance.Therefore, this embodiment is not good at expressing the distances ofthe links continuously and needs to approximate the distances assomewhat discrete values. However, the physical phase is not computed,and hence even with the current CPU that is good at serial processing,the computation time may be reduced significantly. This is a great meritof this embodiment. As with the first embodiment, the computation iseasily parallelized, and hence it is further preferred to use a GPGPUfor computation.

In the above description, every link in the network has a uniformtransmission speed, but this embodiment may be used even when linkshaving different transmission speeds are mixed. For example, consideringLink L1 having the distance of 2 and the transmission speed of 1 andLink L2 having the distance of 4 and the transmission speed of 2, eventhough the distance of Link L2 is twice that of Link L1, thetransmission speed of Link L2 is also twice that of Link L1, and henceit is considered that the periods of time required for the signal topass through Link L1 and Link L2 are the same. In consideration of this,when the distance of each link multiplied by a factor that isproportional to the reciprocal of the transmission speed of the link iscalled a real distance, the real distance of each link may be determinedbefore setting the unit of distance so that the unit of distance is setbased on the real distance. The thus-determined unit of distance iscalled a real unit of distance. A value obtained by approximating thereal distance of the link by an integer multiple of the real unit ofdistance is set as an upper limit value of the counter of the link. Inthis manner, this embodiment may be applied also to the network in whichlinks having different transmission speeds are mixed.

In the above description, the counter adds 1 to the count value everyunit of time, but the counter may subtract instead. Specifically, toeach link in the network, a counter value that is proportional to thedistance of the link is set in advance, and the counter is activated inresponse to the signal reaching a node at one end of the link. Theactivated counter subtracts the count value by 1 each time one unit oftime is elapsed. When the count value becomes zero, it is consideredthat the signal has reached a node at the other end of the link.

Further, the counter is used this time to transmit virtual phasetransmission information, but as long as “information that the phase hasbeen transmitted” to be used can be correlated with the physicaltransmission of the phase, similar effects as those of the invention ofthe subject application can be obtained.

Example 1

Next, a path selection device 10 according to Example 1 of thisinvention is described with reference to FIG. 10. The path selectiondevice 10 includes a network information acquisition unit 11, a networkstate analysis unit 12, a propagation direction identification unit 13,and a network path selection unit 14. The path selection device 10 andthe units 11 to 14 are realized as a computer that operates inaccordance with a program stored in a storage device, and morespecifically constitutes, for example, a part of a server of an internetaccess provider or a router.

The network information acquisition unit 11 includes a network interfacedevice, and acquires the overall image information of the network,specifically, the topology information of the network and the coupledstate information of the network from the network.

The most prominent feature of the invention of the subject applicationis the network state analysis unit 12. The network state analysis unit12 may include the propagation direction identification unit 13, and inthis example, a case where the propagation direction identification unit13 is mounted therein is illustrated.

The role of the network state analysis unit 12 is to process theinformation on the coupled state of the network acquired by the networkinformation acquisition unit 11 into information with which the networkpath selection unit 14 may perform the path selection. The processingperformed by the network state analysis unit 12 is the device thatexecutes the path selection processing by the path selection methoddescribed in the first embodiment. In other words, in the networkincluding as the nodes the oscillators which move in accordance with theequation capable of describing the diffusion of the oscillation and areconnected via links that transmit the oscillation depending on thephysical quantity indicating the connectibility of the nodes, thefollowing processing is executed: the process in which the oscillationin the oscillator corresponding to the start node is transmitted to theother oscillators is simulated to determine the first link of each ofthe nodes; and a tree structure (for example, as the one on the rightside of FIG. 3) is determined from the network topology (for example, asthe network overview on the right side of FIG. 3) prepared in advanceand the first link of each of the nodes. The start node is a server, arouter, or the like including the path selection device 10. In thisexample, the phase transmission by the nonlinear oscillators is used. AVan der Pol oscillator is used as the nonlinear oscillator.

As described above with reference to FIGS. 5 and 6, the propagationdirection identification unit 13 is a part for monitoring the statusesof the virtual links for the outward path and the inward path providedto each link. The network state analysis unit 12 uses monitoringinformation of the virtual links obtained by the propagation directionidentification unit 13 to generate the tree structure as illustrated inFIG. 3. In this example, the example of performing the shortest pathsearch is illustrated, but as described in the Effect of the Inventionsection, the invention of the subject application may be applied to aselection of various paths by storing the phase transmission times fromthe links.

The network path selection unit 14 selects and outputs, based on thetree structure determined by the network state analysis unit 12, theshortest path from the node device serving as the start node, such asthe server, the router, or the like including the path selection device10 to the node device serving as the target node, which is specified byan external program or an input device.

FIG. 11 illustrates an example of the network for which the shortestpath search is performed in this example. A cubic network is constructedand used with the number of nodes being N. Further, in this example, thedistances (diffusion coefficients D) of all the links are the same.

This example is an example in which physical phases of a plurality ofnonlinear oscillators are computed, and hence the computation is slowwith a single normal CPU. Therefore, in this example, a GPGPU was usedto perform parallel computation. The general purpose graphic processingunit (GPGPU) is a graphics processor that can be used for generalpurpose, and is a processor which is capable of realizing super parallelcomputation with an inexpensive board and is attracting attention inrecent years. The GPGPU is attracting attention because thecomputational performance of a single CPU has already peaked, and thereis no other way to increase the total computation performance than toperform simple processing in a super parallel fashion. As in theembodiment of the subject application, an algorithm suitable forparallel computation in which each process (computation by eachnonlinear oscillator) may be performed independently is expected to be amainstream in the future with the aid of the GPGPU or the like. Thealgorithms such as the Dijkstra method that have conventionally beenused are not suitable for parallel computation.

When this example was performed with the above-mentioned conditions toperform the shortest path search from an arbitrary start node to all theother nodes, a reasonable output of the tree structure was obtained.

FIG. 12 shows the results of the computation speeds of the Dijkstramethod and this example dependent on the number of nodes. Thecomputation speed is calculated as being normalized with the computationtime of this example at 1,000 nodes. In this example, faster computationresult than that of the conventional Dijkstra method is obtained as thenumber of nodes becomes larger. This shows that the invention of thesubject application is a very effective path selection method.

Example 2

A path selection device according to Example 2 of this invention isdescribed. This example corresponds to the second embodiment. The pathselection device in this example also has a similar configuration asthat of the path selection device of Example 1, and hence is describedwith reference to FIG. 10.

In this example, the network state analysis unit 12 does not compute thephase transmission by the nonlinear oscillators but performs simulationcorresponding to the second embodiment. Specifically, with the time whenthe signal is transmitted from the start node as a starting point, theposition of the signal on the link for each unit of time is computed todetermine the first link and the like of each node.

In the first embodiment, the computation necessary for the simulation iseasily parallelized and hence the simulation is executed with the GPGPUin Example 1, but in the second embodiment, not only the parallelizationof the computation is easy but also the computational load required forthe simulation is low, and hence the computation speed is increased evenwith a CPU that is not parallelized. In order to clarify this effect, aresult obtained by using a general CPU is shown in the graph. Note that,the second embodiment is also easy to parallelize, and when thecomputation processing is parallelized and implemented by a GPGPU, afurther increase in speed may be realized.

The used network is the same cubic network as illustrated in FIG. 11similarly to Example 1. Further, the conditions are that the distancesof all the links are the same and that information reaches the adjacentnode after one time. When this example was performed with theabove-mentioned conditions to perform the shortest path search from anarbitrary start node to all the other nodes, a reasonable output of thetree structure was obtained.

FIG. 13 shows the results of the computation speeds of the Dijkstramethod and this example dependent on the number of nodes. Thecomputation speed is calculated as being normalized with the computationtime of this example at 1,000 nodes. In this example, faster computationresult than that of the conventional Dijkstra method is obtained.

It has been described in the description of the first and secondembodiments that the method of this invention operates on theprecondition that the overall image of the network is known correctly tosome extent. At that time, it has been expected that a question as towhether the overall image of the network needs to be grasped correctlywould arise. In order to answer such question, a simple simulation asdescribed below was performed. This is described with reference to FIG.14.

In this simulation, when the information is transmitted from the startnode to the target node, the path selection device 10 in this example isused to select the shortest path to the target node, and the informationis transmitted along the shortest path. In the overall image informationof the network used when the path selection device 10 determines theshortest path, a node in which a fault occurs does not exist in thenetwork. The links constituting the shortest path determined at thistime are illustrated by thick lines in the figure.

In a period from when the information is transmitted from the start nodeuntil the information arrives at the target node, it is assumed asillustrated in FIG. 14 that a fault has occurred in a node on thepreviously determined shortest path. At this time, a need to notify thenodes in the network of faulty node information arises. The faulty nodeinformation is finally transmitted to all the nodes, and the overallimage information of the network in all the nodes is updated. However,immediately after the fault has occurred, the overall image informationof the network may be updated only in the nodes surrounding the node inwhich the fault has occurred, and cannot be updated in distant nodes.

On the other hand, the nodes that have received the informationtransmitted by the start node transfer the information along theshortest path to the target node, the shortest path being determinedbased on the overall image information of the network that has beenacquired by the node to that time point.

When the simulation was performed on the above-mentioned preconditions,it was confirmed that an intermediate node detected the failure that hadnot been known at the time when the start node had transmitted theinformation, and thereafter, the information is transmitted along theshortest path determined based on the updated overall image informationof the network. In this manner, according to this invention, the networkmay autonomously avoid the failure and transmit the information to thetarget node.

Such effects may be obtained because, according to the path selectionmethod of this invention, the path selection may be executed at veryhigh speed, and hence the path selection computation that has not beenexecutable at high frequency can be executed every time the nodestransmit information. Further, when the path selection processing basedon the path selection method of this invention is performed as describedabove in each node of the network every time the node transmitsinformation, a network that avoids a failure autonomously may beprovided. As described above, the path selection method according tothis invention is a very effective path selection method that is notlimited to the simple high-speed operation.

This invention has been described above by way of the embodiments andthe examples, but this invention is not limited thereto, and variousmodifications may be made without changing the technical meaning of thisinvention.

For example, the above-mentioned embodiments and examples have beendescribed taking the information network as an example of the network,but this invention is not limited to the type of the network and may beapplied, for example, to the path selection in the traffic network.

Further, in the above description, the case where the shortest pathsearch is performed has been mainly described, but processing satisfyingrequests for a selection of various paths such as the second shortestpath and the third shortest path is also possible.

Further, in the above description, the distance of the link has beenused as the coupled state information of the network, and hence theselected path has been the shortest path, but the coupled stateinformation of the network is not limited to the distance of the link.For example, a selection of a desired path may be performed with thespeed, capacity, and the like of the information flow through the linkbeing used as the coupled state information.

Further, in the first embodiment and Example 1, the nodes are likened tothe nonlinear oscillators, but for example, the phase may be transmittedby using a soliton. This application is based on and claims the benefitof priority from Japanese Patent Application No. 2010-259345, filed onNov. 19, 2010, the entire disclosure of which is incorporated herein byreference.

1.-33. (canceled)
 34. A path selection device, comprising: networkinformation acquisition means for acquiring, by a start node which is asource of an oscillation or a signal to be simulated regarding atransmission process in a network and is one node in the network,coupled state information of the network indicating a connectibility ofnodes in the network from the network; network state analysis means fordetermining, by an arithmetic unit of the start node executing thesimulation in accordance with a computational model constructed based onthe coupled state information, when n (n is a natural number) linksconnected to the one node in the network are called a first link, asecond link, . . . , an n-th link in order from a link that hastransmitted the oscillation or the signal first to the one node, atleast the first link for each of the nodes in the network; and networkpath selection means for selecting by the start node a path that extendsfrom a target node, which is one node in the network other than thestart node, to the start node via the first link of intermediate nodesas a desired path between the start node and the target node.
 35. A pathselection device according to claim 34, wherein the computational modelcomprises a computational model in which the nodes in the network arelikened to oscillators that oscillate in accordance with an equationdefined based on the coupled state information and transmit theoscillation to each other via a link between the nodes, wherein thestart node is formed into the computational model as an oscillator thatmoves as a source of the oscillation, and wherein a physical phase ofeach of the oscillators is simulated, to thereby simulate transmissionof the oscillation from the oscillator of the start node to otheroscillators.
 36. A path selection device according to claim 35, whereinthe oscillator is formed into the computational model as a nonlinearoscillator, wherein an initial value of a frequency of the oscillator ofthe start node has a higher frequency than initial values of theoscillators of other nodes than the start node, and wherein thetransmission of the oscillation from the oscillator of the start node tothe other oscillators is detected based on frequency matching with theoscillator of the start node due to an entrainment phenomenon of thefrequency.
 37. A path selection device according to claim 35, whereinthe transmission of the phase to a node is detected based on a change inamplitude of the node.
 38. A path selection device according to claim35, wherein in order to detect the transmission of the oscillation inone direction along a link, a motion of a virtual oscillator that doesnot correspond to the nodes is included in the simulation.
 39. A pathselection device according to claim 34, which is a computational modelin which every link in the network is divided into a number of sections,the number being determined based on a physical quantity regarding thelink, and one of the number of sections and a unit of time arecorrelated to simulate a propagation state of the signal in the network.40. A path selection device according to claim 39, wherein thecomputational model approximates the physical quantity of each link asan integer multiple of a value indicating a unit physical quantity,which is the physical quantity regarding one link per unit of time, andmodels movement of the signal assuming that the physical quantitychanges discretely in steps of the unit physical quantity every time theunit of time is elapsed, and wherein a counter which starts countingfrom a time when the signal enters a corresponding link, increments acount by one every time the unit of time is elapsed, and counts up to avalue corresponding to the physical quantity of the corresponding linkis provided so as to correspond to each link of the network.
 41. A pathselection device according to claim 40, wherein the physical quantity ofthe link comprises a distance of the link, and the unit physicalquantity comprises a distance by which the signal originating from thestart node moves in the link in the unit of time.
 42. A path selectiondevice according to claim 41, wherein as the distance of the link, avalue obtained by multiplication with a coefficient that is proportionalto a reciprocal of a transmission speed of the link is used.
 43. A pathselection device according to claim 39, wherein in association with eachlink in the network, operations of a counter corresponding to onedirection along the link and a counter corresponding to anotherdirection than the one direction are included in the simulation.
 44. Anon-transitory tangible medium storing a program for causing a computerto function as: network information acquisition means for acquiring, bya start node which is a source of an oscillation or a signal to besimulated regarding a transmission process in a network and is one nodein the network, coupled state information of the network indicating aconnectibility of nodes in the network from the network; network stateanalysis means for determining, by an arithmetic unit of the start nodeexecuting the simulation in accordance with a computational modelconstructed based on the coupled state information, when n (n is anatural number) links connected to the one node in the network arecalled a first link, a second link, . . . , an n-th link in order from alink that has transmitted the oscillation or the signal first to the onenode, at least the first link for each of the nodes in the network; andnetwork path selection means for selecting by the start node a path thatextends from a target node, which is one node in the network other thanthe start node, to the start node via the first link of intermediatenodes as a desired path between the start node and the target node. 45.A non-transitory tangible medium according to claim 44, wherein thecomputational model comprises a computational model in which the nodesin the network are likened to oscillators that oscillate in accordancewith an equation defined based on the coupled state information andtransmit the oscillation to each other via a link between the nodes,wherein the start node is formed into the computational model as anoscillator that moves as a source of the oscillation, and wherein aphysical phase of each of the oscillators is simulated, to therebysimulate transmission of the oscillation from the oscillator of thestart node to other oscillators.
 46. A non-transitory tangible mediumaccording to claim 42, wherein the oscillator is formed into thecomputational model as a nonlinear oscillator, wherein an initial valueof a frequency of the oscillator of the start node has a higherfrequency than initial values of the oscillators of other nodes than thestart node, and wherein the transmission of the oscillation from theoscillator of the start node to the other oscillators is detected basedon frequency matching with the oscillator of the start node due to anentrainment phenomenon of the frequency.
 47. A non-transitory tangiblemedium according to claim 45, wherein the transmission of the phase to anode is detected based on a change in amplitude of the node.
 48. Anon-transitory tangible medium according to claim 45, wherein in orderto detect the transmission of the oscillation in one direction along alink, a motion of a virtual oscillator that does not correspond to thenodes is included in the simulation.
 49. A non-transitory tangiblemedium according to claim 44, which is a computational model in whichevery link in the network is divided into a number of sections, thenumber being determined based on a physical quantity regarding the link,and one of the number of sections and a unit of time are correlated tosimulate a propagation state of the signal in the network.
 50. Anon-transitory tangible medium according to claim 49, wherein thecomputational model approximates the physical quantity of each link asan integer multiple of a value indicating a unit physical quantity,which is the physical quantity regarding one link per unit of time, andmodels movement of the signal assuming that the physical quantitychanges discretely in steps of the unit physical quantity every time theunit of time is elapsed, and wherein a counter which starts countingfrom a time when the signal enters a corresponding link, increments acount by one every time the unit of time is elapsed, and counts up to avalue corresponding to the physical quantity of the corresponding linkis provided so as to correspond to each link of the network.
 51. Anon-transitory tangible medium according to claim 50, wherein thephysical quantity of the link comprises a distance of the link, and theunit physical quantity comprises a distance by which the signaloriginating from the start node moves in the link in the unit of time.52. A non-transitory tangible medium according to claim 51, wherein asthe distance of the link, a value obtained by multiplication with acoefficient that is proportional to a reciprocal of a transmission speedof the link is used.
 53. A non-transitory tangible medium according toclaim 49, wherein in association with each link in the network,operations of a counter corresponding to one direction along the linkand a counter corresponding to another direction than the one directionare included in the simulation.
 54. A network system, comprising aplurality of nodes with any one of computers being a node, the any oneof computers comprising the path selection device according to claim 34,and operating in accordance with a program stored in a non-transitorytangible medium.
 55. A network system according to claim 54, whereineach of the plurality of nodes determines, each time information istransmitted to nodes other than the node, when the node is the startnode, a desired path between the start node and the target node.
 56. Apath selection method, comprising the steps of: acquiring, by a startnode which is a source of an oscillation or a signal to be simulatedregarding a transmission process in a network and is one node in thenetwork, coupled state information of the network indicating aconnectibility of nodes in the network from the network; determining, byan arithmetic unit of the start node executing the simulation inaccordance with a computational model constructed based on the coupledstate information, when n (n is a natural number) links connected to theone node in the network are called a first link, a second link, . . . ,an n-th link in order from a link that has transmitted the oscillationor the signal first to the one node, at least the first link for each ofthe nodes in the network; and selecting, by the start node, a path thatextends from a target node, which is one node in the network other thanthe start node, to the start node via the first link of intermediatenodes as a desired path between the start node and the target node. 57.A path selection method comprising, each time any one of nodes in thenetwork transmits information to other nodes than the node, with a nodeas a transmission source of the information as the start node, executingthe path selection method according to claim
 56. 58. A path selectionmethod according to claim 56, wherein the computational model comprisesa computational model in which the nodes in the network are likened tooscillators that oscillate in accordance with an equation defined basedon the coupled state information and transmit the oscillation to eachother via a link between the nodes, wherein the start node is formedinto the computational model as an oscillator that moves as a source ofthe oscillation, and wherein a physical phase of each of the oscillatorsis simulated, to thereby simulate transmission of the oscillation fromthe oscillator of the start node to other oscillators.
 59. A pathselection method according to claim 58, wherein the oscillator is formedinto the computational model as a nonlinear oscillator, wherein aninitial value of a frequency of the oscillator of the start node has ahigher frequency than initial values of the oscillators of other nodesthan the start node, and wherein the transmission of the oscillationfrom the oscillator of the start node to the other oscillators isdetected based on frequency matching with the oscillator of the startnode due to an entrainment phenomenon of the frequency.
 60. A pathselection method according to claim 58, wherein the transmission of thephase to a node is detected based on a change in amplitude of the node.61. A path selection method according to claim 58, wherein in order todetect the transmission of the oscillation in one direction along alink, a motion of a virtual oscillator that does not correspond to thenodes is included in the simulation.
 62. A path selection methodaccording to claim 56, which is a computational model in which everylink in the network is divided into a number of sections, the numberbeing determined based on a physical quantity regarding the link, andone of the number of sections and a unit of time are correlated tosimulate a propagation state of the signal in the network.
 63. A pathselection method according to claim 62, wherein the computational modelapproximates the physical quantity of each link as an integer multipleof a value indicating a unit physical quantity, which is the physicalquantity regarding one link per unit of time, and models movement of thesignal assuming that the physical quantity changes discretely in stepsof the unit physical quantity every time the unit of time is elapsed,and wherein a counter which starts counting from a time when the signalenters a corresponding link, increments a count by one every time theunit of time is elapsed, and counts up to a value corresponding to thephysical quantity of the corresponding link is provided so as tocorrespond to each link of the network.
 64. A path selection methodaccording to claim 63, wherein the physical quantity of the linkcomprises a distance of the link, and the unit physical quantitycomprises a distance by which the signal originating from the start nodemoves in the link in the unit of time.
 65. A path selection methodaccording to claim 64, wherein as the distance of the link, a valueobtained by multiplication with a coefficient that is proportional to areciprocal of a transmission speed of the link is used.
 66. A pathselection method according to claim 62, wherein in association with eachlink in the network, operations of a counter corresponding to onedirection along the link and a counter corresponding to anotherdirection than the one direction are included in the simulation.